The problem with ABA therapy is that the "targets" you (or they) choose to work on may well be unhelpful or traumatising. E.g. lots of therapists will target things like eye contact, or suppressing stims (e.g. running back and forth or lying on the floor looking at his car). But this kind of misses the point: eye contact is something that lots of neurotypical people find aids conversation. Most autistic people find it is either not helpful or actively unhelpful. So yes, you can train an autistic person to give eye contact - but it is likely to distract rather than aid the "bigger goal" of actual communication. Similarly you can train somebody out of a stim: but the stim is there to meet a need - so unless you find another way to meet the need instead then getting rid of the stim is harming the person.
We actually did do ABA with our daughter when she was little (distance based - so we "did" the "therapy", guided by a consultant). In some ways it was helpful (we learned how to break things down into small steps, and how to model things - neither of which are specifically ABA but our therapist was more generally helpful). But there were points where they asked e.g. if we would like to target removing a stim, or they were asking us to measure things that just seemed objectively unmeasurable, that I started to question it and lose confidence.
I know it's really reassuring to have an outside "expert" guiding you (I get it, that's what we did). But it's very expensive, a lot of the advice will just be parenting, and some of it may be actively harmful unless you are very careful and really do your research. Given your DS seems to be doing pretty well overall, I think people are just worried that the risks would potentially really outweigh the benefits.
I would stay on all the NHS lists and see if he gets a Dx and what help is available. In the meantime, see if there are any local Facebook groups supporting SEN parents - you may be able to meet some people locally that way to connect with, which is always helpful when you have worries. The Nurturing Neurodiversity Facebook group is also useful for connecting with other parents who suspect their kids are autistic (many of them also young kids, pre-diagnosis).
Honestly my daughter still (age 7) often doesn't answer to her name. In fact, looking back this was one of her targets in ABA and obviously it wasn't very effective. I still have to ask her about 5 times what she wants for breakfast. I don't think she's ever in her life told me she's hungry or thirsty (unlike DS who is 4 and will remind me of his needs on an almost constant basis :). She's just wrapped up in what she's interested in. A bit the "absent minded professor type", you know? I can almost see the tendrils....: the-art-of-autism.com/why-its-hard-to-switch-tasks-a-comic-strip-explanation/
It can be frustrating as a parent (even though I'm very similar myself). But so far at least it hasn't held her back from making friends or doing well at school (and she hasn't actually expired of hunger or thirst), so I try not to worry too much. As she gets older I think experience will teach her when she needs to have her "radar" on for external stimuli, and when she can safely focus on her activity to the exclusion of everything else. I think/hope that's what I've now learned to do as an adult - it just takes time.